Distance, Speed and Time

Convert the following speed units:

1. Change 33km/h to a) km/min b) m/h2. Change 100m/s to a) km/s b) m/min3. Change 40m.p.h to a) miles/min b) miles/s4. Change 90km/h to a) km/s b) m/s5. Change 100m/s to a) m/h b) km/h

Distance Time Graphs

Draw distance time graphs to show the following journeys. Show the required working and where necessary, give answers correct to 3s.f.

1. A train leaves from York and travels at 40km/h for 3 hours. It stops for half an hour and then returns back to York at 50km/h. Draw a graph to illustrate this journey. Use 2cm for 1 hour and 2cm for 50km. What is the average speed for a) the journey before going back to York?b) the whole journey?

2. A cyclist leaves home and rides at 15km/h for 2 hours. He rests for ½ hour and then continues riding away from home at 12km/h for 1 ½ hours. He has another rest of ½ hour before returning home, without stopping, at 20km/h. a) For how long is the cyclist away from home?b) Draw a graph to illustrate this journey. Use 2cm for 1 hour and 1cm for 10km.c) What is the average speed for the journey before going back to home?d) What is the average speed for the whole journey?

3. A bus leaves the bus station at 10:00a.m. It travels at 30km/h for ½ hour, then stops for 12 minutes, before continuing at 40km/h for 2 hours.a) How far has the bus travelled from the bus station now?b) Draw the graph to illustrate the journey. Use 2cm for 1 hour and 1cm for 10km.c) What is the average speed for the whole journey?

4. A family travel by car from town A to town B 50km away, in 48 minutes. They stop in town B for 1 hour and then continue to village C, which is 70km from B, at a speed of 50km/h. The family stop at C for 2 hours and then return, without stopping, along the same route to A at 60km/h.a) Draw the graph to illustrate the journey. Use 3cm for 1 hour and 1cm for 10km.b) What is the speed of the journey from A to B and the time taken for the return

journey from C to A?

Velocity Time Graphs

Worked example: A car accelerates from rest at 5m/s2 for 6 seconds and then travels at a constant velocity for 10 seconds after which it decelerates to rest at 3m/s2. Represent this information by drawing a velocity time graph. Use 2cm for 5 seconds and 2cm for 5m/s.

1. From O to A, the car reached a velocity of 30m/s after 6 seconds (Acceleration of 5m/s2

means that the velocity is increasing by 5m/s every second for 6 seconds where the velocity reached will be 5m/s × 6 = 30m/s). Gradient of OA represents the acceleration (Acceleration = Velocity ÷ Time or Change in y value ÷ Change in x value).

2. From A to B, the car is moving at constant velocity (i.e. 30m/s where gradient of AB is zero and therefore, no acceleration)

3. From B to C down to the time axis, where C is 3 units down the velocity axis (i.e. 3m/s) and 1 unit along the time axis (i.e. 1 sec) from B. Thus, a deceleration of 3m/s2 (Gradient of BC is -3, that is, a deceleration of 3m/s2).

Examples on Velocity Time Graphs

1. The velocity-time graph illustrates the journey of a car between a set of traffic-lights and a zebra crossing.

a) What is the car’s acceleration for the first 4 seconds?b) What happens when t = 4?c) For how long is the car moving at a constant velocity? d) For how long is the car braking? e) What is the deceleration of the car?f) For how long is the car moving?

2. The velocity-time graph illustrates the first 7 minutes of the flight of a rocket.

a) What is the initial acceleration of the rocket?b) What is the velocity of the rocket 2 minutes after its launch?c) What is the steady velocity obtained by the rocket?d) What is the acceleration of the rocket during the fourth minute of its flight?

3. This velocity-time graph illustrates the journey of a train between two stations.

a) What is the acceleration for the first 2 minutes in km/h2?b) What is the greatest velocity of the train?c) For how long is the train travelling at constant velocity?d) What is the acceleration during the third minute km/h2?e) What is the deceleration of the train km/h2?

For question 4 to 6, draw a velocity-time graph to illustrate the following journeys. Use 1cm for 1 second and 2cm for 5m/s.

4. A car accelerates steadily from rest reaching a velocity of 12m/s in 10 seconds.

5. A train accelerates from rest reaching a velocity of 8m/s in 5 seconds and then immediately decelerates to rest in 4 seconds.

6. A motor bike accelerates from rest to a velocity of 20m/s in 4 seconds, maintains this steady velocity for 8 seconds and then decelerates to rest in 5seconds.